Thanks for your reply and that suggestion. I will hope to do a mixture of rides, probably in the 50 mile up to 100 mile range. Not too many 100 milers so I can keep it going day after day Will be starting and finishing in the Hakata station area. So far I've just been getting ideas by looking at the Strava heatmaps and popular segments.
When I was living in Fukuoka (I spent one year at Kyushu University as a postdoc), I was located on Ito-shima, so I can't tell you much about the routes to the East of Fukuoka (they just didn't make sense at the time). You can either follow the coast line which is not completely flat (on my standard running route I got ~200 m of elevation in over 8~14 km) or venture inwards for some more hills. I don't remember any proper mountains in the immediate vicinity, but if you are willing to ride 150 km, you'll get your fair share of climbing. Another advantage is that you don't really have to worry about snow and ice.
Sadly Mount Sefuri is closed at the moment, from the Fukuoka side, as is the Itaya Pass another stable climb in Fukuoka city. However, AFAIK Sefuri can still be climbed from the Saga side up Route 305. If you want climbing and quiet roads, just south of your Itoshima courses, but running parallel are some very nice forest roads which lead into Saga prefecture. They can be reached via Route 12 or Route 564. See Heatmap for details.